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Fractions ChallengeLevel C
JUMPMath
Copyright © 2013 JUMP Math
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JUMP MathOne Yonge Street, Suite 1014Toronto, Ontario M5E 1E5Canadawww.jumpmath.org
Writer: Dr. John MightonCover Layout: Gabriella KerrCover Photograph: © iStockphoto.com/Stéphane Bidouze
ISBN 978-1-927457-22-1
Printed and bound in Canada
Name: _______________________________ Date: _______________
page 1
Fractions Challenge – Level C
Worksheet Counting by 2, 3 and 5 F-1 1. Complete the following hands: BONUS: Try to do it when the top of this page is covered!
2 3
5
6 9
5 25
4 8
Name: _______________________________ Date: _______________
page 2
Fractions Challenge – Level C
Worksheet Counting by 2, 3 and 5 F-1 (con’t) 1. Complete the following questions. (Hint: Use your 2 hand)
3 2 = _____
1 2 = _____
4 2 = _____
3 2 = _____
1 2 = _____
5 2 = _____
2 2 = _____
4 2 = _____
2. Complete the following questions. (Hint: Use your 3 hand)
3 3 = _____
2 3 = _____
4 3 = _____
3 3 = _____
1 3 = _____
3 3 = _____
5 3 = _____
2 3 = _____
3. Complete the following questions. (Hint: Use your 5 hand)
3 5 = _____
2 5 = _____
4 5 = _____
3 5 = _____
1 5 = _____ 3 5 = _____
5 5 = _____
2 5 = _____
4. Diagnostic Quiz: Complete the following questions.
3 3 = _____
2 2 = _____
4 5 = _____
4 2 = _____
1 5 = _____
3 5 = _____
2 5 = _____
5 3 = _____
3 2 = _____
2 3 = _____
4 3 = _____
2 2 = _____
1 3 = _____
3 5 = _____
4 5 = _____
5 5 = _____
5 3 = _____
1 2 = _____
2 2 = _____
1 5 = _____
BONUS:
1 8 = _____
1 21 = _____
1 23 = _____
1 296 = _____
1 663 = _____
1 0 = _____
1 1 = _____
1 12,035 = _______
46 1 = _____
127 1 = _____
2 0 = _____
0 189 = _____
1,905 1 = ________
104,761 0 = _____
0 1 = _____
1 6 = _____
TEACHER: Do not move on until all of your students have gotten 100% on the diagnostic quiz (Q 4) on this page. Make sure your students can add and subtract one digit numbers as taught in the Appendix in the Teacher Manual. Students can learn the skills required to do well in this unit very quickly—do not move on until you have taught the skills covered in this section.
Name: _______________________________ Date: _______________
page 3
Fractions Challenge – Level C
Worksheet Exploring Fractions F-2 1. Name the following fractions a) b) c) d)
e) f) g) h)
i) j) k) l)
2. Shade the fractions named a) 1 b) 1 c) 3 2 3 4 d) 3 e) 2 f) 5 6 5 9
Name: _______________________________ Date: _______________
page 4
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions F-3 A 1. Add 1 + 1 2 + 3 2 + 1 3 3 7 7 11 11 2 + 2 2 + 3 3 + 4 5 5 11 11 8 8 3 + 2 1 + 4 4 + 3 17 17 21 21 9 9 2. Subtract 3 - 1 2 - 1 4 - 2 5 5 7 7 11 11 5 - 2 6 - 2 5 - 1 8 8 17 17 9 9 3. Advanced 1 + 1 + 1 1 + 2 + 3 1 + 2 + 5 7 7 7 7 7 7 15 15 15 BONUS: 2 + 5 - 3 11 11 11
Name: _______________________________ Date: _______________
page 5
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions F-3 B 1. Add 1 + 2 4 + 2 3 + 7 4 4 7 7 11 11 8 + 3 5 + 11 12 + 13 17 17 19 19 32 32 2. Subtract 7 - 1 8 - 7 10 - 3 11 11 10 10 15 15 15 - 12 16 - 3 5 - 1 19 19 17 17 9 9 3. Advanced 3 + 2 + 1 5 + 3 + 8 3 + 1 + 2 + 5
7 7 7 17 17 17 12 12 12 12 BONUS: 8 + 2 - 5 9 - 2 - 1 12 + 11 - 8 11 11 11 11 11 11 35 35 35
Name: _______________________________ Date: _______________
page 6
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions (Warm-Up) F-4 A TEACHER: If your students find the material on pages 8 and 9 easy they don’t have to do every question. They can do one or two of each type and then move on to page 10. We recommend that younger students do every question. 1. Write times signs beside the fractions:
Example: 15 +
13
15 +
13
12 +
13
12 +
15
13 +
15
23 +
12
23 +
15
25 +
13
2. Switch the bottom numbers:
Example: 15 +
13
15 +
13
12 +
13
12 +
15
13 +
15
23 +
12
23 +
15
25 +
13
35 +
12
45 +
12
23 +
25
3. Write times signs and switch the numbers:
Example: 15 +
13
15 +
13
15 +
13
12 +
13
12 +
15
13 +
15
23 +
12
23 +
15
25 +
13
35 +
12
45 +
12
23 +
25
3 5 5 3
3 5 5 3
Name: _______________________________ Date: _______________
page 7
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions (Warm-Up) F-4 A (con’t) 4. Write an equal sign and draw lines for the new fractions:
Example: 15 +
13
15 +
13
= — + —
12 +
13
12 +
15
13 +
15
23 +
12
23 +
15
25 +
13
35 +
12
45 +
12
23 +
25
5. Perform the multiplications:
Example: 15 +
13
15 +
13
= — + — = 315 +
515
12 +
13
= — + —
12 +
15
= — + —
13 +
15
= — + —
23 +
12
= — + —
23 +
15
= — + —
25 +
13
= — + —
35 +
12
= — + —
45 +
12
= — + —
23 +
25
= — + —
3 5 5 3
3 5 5 3
3 5 5 3
3 2 2 3
5 2 2 5
5 3 3 5
2 3 3 2
5 3 3 5
3 5 5 3
2 5 5 2
2 5 5 2
5 3 3 5
3 2 2 3
5 2 2 5
5 3 3 5
2 3 3 2
5 3 3 5
3 5 5 3
2 5 5 2
2 5 5 2
5 3 3 5
3 5 5 3
Name: _______________________________ Date: _______________
page 8
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions (Warm-Up) F-4 A (con’t)
6. Perform the additions:
Example: 15 +
13
15 +
13
= 315 +
515 =
315 +
515 =
815
12 +
13
= 36 +
26 = —
12 +
15
= 510 +
210 = —
13 +
15
= 515 +
315 = —
23 +
12
= 46 +
36 = —
23 +
15
= 1015 +
315 = —
25 +
13
= 615 +
515 = —
35 +
12
= 610 +
510 = —
45 +
12
= 810 +
510 = —
23 +
25
= 1015 +
615 = —
7. Perform the multiplications and the additions:
Example: 15 +
13
15 +
13
15 +
13
= — + — = 315 +
515 =
315 +
515 =
815
12 +
13
= — + — = —
12 +
15
= — + — = —
13 +
15
= — + — = —
23 +
12
= — + — = —
23 +
15
= — + — = —
25 +
13
= — + — = —
35 +
12
= — + — = —
45 +
12
= — + — = —
23 +
25
= — + — = —
3 5 5 3
3 5 5 3
3 2 2 3
5 2 2 5
5 3 3 5
2 3 3 2
5 3 3 5
3 5 5 3
2 5 5 2
2 5 5 2
5 3 3 5
3 2 2 3
5 2 2 5
5 3 3 5
2 3 3 2
5 3 3 5
3 5 5 3
2 5 5 2
2 5 5 2
5 3 3 5
3 5 5 3
3 5 5 3
3 5 5 3
Name: _______________________________ Date: _______________
page 9
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions F-4 A (con’t) 8. Add 1 + 1 1 + 1 1 + 1 2 3 3 5 2 5 9. Advanced 2 + 1 3 + 1 2 + 1 5 3 5 2 3 2 1 + 2 4 + 1 2 + 2 5 3 5 2 3 5 BONUS: 1 - 1 2 - 1 3 - 1 2 3 3 2 5 2
Name: _______________________________ Date: _______________
page 10
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions F-4 B 1. Add 1 + 1 1 + 1 1 + 1 3 5 3 4 5 6 2. Advanced 2 + 3 1 + 2 1 + 2 5 4 5 3 6 5 3 + 4 1 + 5 3 + 2 4 5 5 6 4 3 BONUS: 3 - 2 3 - 1 5 - 3 4 3 5 4 6 5
Name: _______________________________ Date: _______________
page 11
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions F-4 C 1. Add 1 + 1 1 + 1 1 + 1 3 7 5 8 9 4 2. Advanced 2 + 1 2 + 2 5 + 1 3 7 5 9 7 6 3 + 2 1 + 2 1 + 4 4 7 8 3 7 9 BONUS: 3 - 1 5 - 3 5 - 1 4 7 7 8 9 7
Name: _______________________________ Date: _______________
page 12
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions (Warm Up) F-5 A 1. Write how many times the lesser denominator goes into the greater denominator:
Example: 12 +
110
12 +
110
12 +
110
15 +
110
12 +
18
13 +
16
15 +
120
12 +
16
25 +
125
35 +
115
12 +
78
2. Change the fraction with the lesser denominator and keep the other fraction the same:
Example: 12 +
110
12 +
110
12 +
110
= 510 +
110
12 +
110
15 +
110
12 +
18
13 +
16
15 +
120
12 +
16
25 +
125
35 +
115
12 +
78
5 5
5 5
5 5
Name: _______________________________ Date: _______________
page 13
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions F-5 A (con’t) 3. Add (Remember: change only one denominator) 1 + 1 1 + 1 1 + 1 2 10 5 10 2 8 1 + 1 1 + 1 1 + 1 3 6 5 20 2 6 4. Advanced 2 + 1 2 + 1 3 + 2 3 15 5 10 5 15 2 + 1 1 + 3 1 + 3 3 12 4 8 4 12 3 + 1 4 + 1 3 + 4 4 2 25 5 15 5 BONUS: 7 - 1 3 - 1 1 - 3 20 5 8 4 2 10
Name: _______________________________ Date: _______________
page 14
Fractions Challenge – Level C
Worksheet Adding and Subtracting Fractions F-5 B 1. Add 1 + 1 1 + 1 1 + 1 4 12 6 18 7 28 2. Advanced 1 + 3 2 + 4 1 + 2 8 16 7 21 6 24 1 + 3 5 + 7 7 + 1 9 18 6 30 24 8 1 + 11 5 + 2 4 + 5 9 27 12 6 7 42 BONUS: 7 - 1 5 - 1 5 - 3 8 16 21 7 6 48
Name: _______________________________ Date: _______________
page 15
Fractions Challenge – Level C
Worksheet Fractions (Warm-Up) F-6 A
1. Write yes beside the number in bold if you say the number when counting by 2’s. If you don’t, write no.
a) 6 ________
b) 3 ________
c) 9 ________
d) 8 ________
e) 10 ________
f) 4 ________
g) 5 ________
h) 7 ________
2. Write yes beside the given number if you say the number when counting by 3’s If you don’t, write no.
a) 9 ________
b) 4 ________
c) 12 ________
d) 13 ________
e) 6 ________
f) 5 ________
g) 8 ________
h) 14 ________
3. Write yes beside the given number if you say the number when counting by 5’s If you don’t, write no.
a) 10 ________
b) 12 ________
c) 15 ________
d) 8 ________
e) 20 ________
f) 9 ________
g) 14 ________
h) 11 ________
4. Circle the smaller denominator. (The first one has been done for you.)
1 + 1 1 + 1 2 + 1 2 3 3 5 6 2
1 - 1 3 + 1 1 + 1 4 8 5 2 2 8
5. Count by the lesser denominator, and write yes if you say the greater denominator. Write no if you don’t. (The first one has been done for you.)
no _______ _______
1 + 1 1 + 1 2 + 1 2 3 3 5 6 2
_______ _______
1 + 1 3 + 1 1 + 1 4 8 5 2 2 8
_______ _______
1 + 1 3 + 1 1 + 1 2 8 15 3 5 9
Name: _______________________________ Date: _______________
page 16
Fractions Challenge – Level C
Worksheet Fractions (Warm-Up) F-6 A (con’t) 6. Count by the lesser denominator until you reach the greater denominator. Write the number
of fingers you have raised beside the times signs:
yes yes yes s
x 1 + 1 x 1 + 1 x 1 + 1 x 2 6 x 5 10 x 3 9
7. Complete the first step of addition by multiplying each fraction by the opposite denominator:
no no no
x 1 + 1 x x 1 + 1 x x 1 + 1 x x 2 3 x x 2 5 x x 3 5 x
8. Write “yes” or “no” above the following fractions. If you wrote “yes,” then complete the first
step of addition as in Question 6 above. If you wrote “no,” complete the first step as in Question 7 above:
_______ _______ _______
1 + 1 3 + 1 1 + 1 3 5 5 10 2 4
_______ BONUS: _______ _______
1 + 1 3 + 1 1 + 1 3 4 15 5 10 5 9. Add or Subtract (change one denominator or change both –for each question you have to
decide what to do). Start by writing “yes” or “no” above the fraction: _________ _________ _________
1 + 1 2 + 1 2 + 1 4 5 3 5 5 20
BONUS: _________ _________ _________
3 + 4 2 + 3 1 + 1 20 5 15 5 16 4
Name: _______________________________ Date: _______________
page 17
Fractions Challenge – Level C
Worksheet Fractions F-6 B 1. Advanced: Add or Subtract (change one denominator or change both) 1 + 1 2 + 1 1 + 1
3 9 3 5 5 20 1 + 1 1 + 1 1 - 1
2 3 4 5 2 10 1 + 5 3 + 1 1 + 1
4 16 20 4 4 3 2. If the denominators are the same, write “same”, otherwise change one denominator or change both. Then complete the questions. 1 + 1 1 + 3 1 + 1
3 12 4 5 7 7 2 + 1 3 + 7 4 + 3 3 2 11 11 5 20
Name: _______________________________ Date: _______________
page 18
Fractions Challenge – Level C
Worksheet Fractions F-6 C 1. Add or Subtract 1 - 1 1 + 3 2 + 4 4 12 7 7 3 5 7 - 1 3 + 1 1 - 1 25 5 12 4 2 14 1 + 1 1 + 7 7 + 1 6 18 5 40 24 6 1 + 1 5 - 1 1 + 5 6 5 21 7 4 24 2 + 1 5 - 1 1 + 1 7 6 7 4 2 16 BONUS: 5 + 3 4 + 1 3 + 5 8 7 9 27 8 32
Name: _______________________________ Date: _______________
page 19
Fractions Challenge – Level C
Worksheet Fractions (Warm Up) F-7 A 1. Write times signs and numbers where necessary:
Example: 12 +
13 +
16
12 +
13 +
16
12 +
13 +
16
13 +
15 +
115
12 +
14 +
38
14 +
15 +
120
23 +
14 +
112
15 +
310 +
220
2. Write times signs and numbers, and carry out multiplication as needed:
Example: 12 +
13 +
16
12 +
13 +
16
= 36 +
26 +
16
12 +
13 +
16
13 +
15 +
115
12 +
14 +
38
14 +
15 +
120
23 +
14 +
112
15 +
310 +
220
3 3
2 2
3 3
2 2
Name: _______________________________ Date: _______________
page 20
Fractions Challenge – Level C
Worksheet Fractions F-7 A (con’t) 3. Solve completely: 1 + 1 + 3 1 + 1 + 1 2 3 6 3 5 15 1 + 1 + 3 1 + 1 + 5 2 4 8 4 5 20 2 + 1 + 1 1 + 3 + 2 3 4 12 5 10 20 BONUS: 1 + 1 + 1 2 + 1 + 1 2 6 3 3 4 12 3 + 1 + 1 1 + 1 + 1 4 8 2 20 4 5
Name: _______________________________ Date: _______________
page 21
Fractions Challenge – Level C
Worksheet Reducing Fractions (Warm Up) F-8 A 1. Divide:
10 ÷ 5 = 15 ÷ 5 = 20 ÷ 5 = 25 ÷ 5 = 5 ÷ 5 =
8 ÷ 2 = 4 ÷ 2 = 2 ÷ 2 = 6 ÷ 2 = 10 ÷ 2 =
6 ÷ 3 = 9 ÷ 3 = 15 ÷ 3 = 12 ÷ 3 = 3 ÷ 3 =
8 ÷ 4 = 12 ÷ 4 = 16 ÷ 4 = 20 ÷ 4 = 4 ÷ 4 =
2. Write division signs beside the fraction:
Example: 510
510
510
515
525
520
210
26
24
28
3. Write division signs and copy the top number:
Example: 510
510
510
510
515
525
520
210
26
24
28
4. Write division sign, copy the top number, and solve:
Example: 510
510
510 = —
510 =
12
510
515
525
520
210
26
24
28
÷ ÷
÷ ÷
÷ ÷
÷ 5 ÷ 5
÷ 5 ÷ 5
÷ 5 ÷ 5
Name: _______________________________ Date: _______________
page 22
Fractions Challenge – Level C
Worksheet Reducing Fractions F-8 A (con’t) 5. Reduce 5 5 5 5 10 15 25 20 2 2 2 2 10 6 4 8 3 3 3 3 6 15 12 9 4 4 4 4 8 12 20 16 TEACHER: Please check the Teacher Manual Section F-8 before proceeding to the next question. 6. Advanced: Reduce 10 20 15 10 15 25 20 25 4 8 6 4 6 10 8 10 6 9 6 9 9 12 15 15 BONUS: 25 12 10 8 30 15 12 12
Name: _______________________________ Date: _______________
page 23
Fractions Challenge – Level C
Worksheet Reducing Fractions F-8 B 1. Advanced: Reduce 6 6 6 6 12 18 30 24 7 7 7 7 21 14 28 42 8 8 8 8 16 24 40 48 9 9 9 9 27 9 36 54 2. Advanced: Reduce 12 18 14 16 18 24 21 24 21 24 24 35 28 30 32 42 BONUS: Add, then reduce 1 + 1 + 1 1 + 3 + 1 20 4 5 3 12 4
Name: _______________________________ Date: _______________
page 24
Fractions Challenge – Level C
Worksheet Naming Mixed & Improper Fractions (Warm Up) F-10 A 1. Name these fractions:
2. Write how many whole pies are shaded: a)
b)
c)
d)
e)
f)
g)
h)
Name: _______________________________ Date: _______________
page 25
Fractions Challenge – Level C
Worksheet Naming Mixed & Improper Fractions F-10 A (con’t) 3. Write these fractions as mixed fractions. a)
b)
c)
d)
e)
f)
g)
h)
i)
Name: _______________________________ Date: _______________
page 26
Fractions Challenge – Level C
Worksheet Naming Mixed & Improper Fractions F-10 A (con’t) 4. Write these fractions as improper fractions. a)
b)
c)
d)
e)
f)
g)
h)
i)
Name: _______________________________ Date: _______________
page 27
Fractions Challenge – Level C
Worksheet Mixed / Improper Fractions F-10 B 1. Write these fractions as mixed fractions and as improper fractions. a) b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
Name: _______________________________ Date: _______________
page 28
Fractions Challenge – Level C
Worksheet Mixed / Improper Fractions F-10 B (con’t) 2. Write these fractions as mixed fractions and as improper fractions. a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
Name: _______________________________ Date: _______________
page 29
Fractions Challenge – Level C
Worksheet Mixed / Improper Fractions F-10 C 1. Shade one piece at a time until you have shaded the amount of pie given in bold. There may be
more pies than you need:
a) 2 12
b) 3 12
c) 1 12
d) 2 23
e) 3 13
f) 2 34
g) 3 14
h) 3 23
2. Draw these mixed fractions. HINT: Draw one pie at a time and colour in the pieces. Keep
drawing pies and shading pieces until you have shaded the correct amount of pie.
2 14
3 14
2 34
1 13
3 12
3 23
Name: _______________________________ Date: _______________
page 30
Fractions Challenge – Level C
Worksheet Mixed / Improper Fractions F-10 C (con’t) 3. Shade one piece at a time until you have shaded the amount of pie given in bold. There may be
more pies than you need:
a) 52
b) 72
c) 83
d) 134
e) 94
f) 32
g) 73
h) 154
4. Draw these improper fractions: HINT: Draw one pie at a time and colour in the pieces. Keep
drawing pies and shading pieces until you have shaded the correct amount of pie.
52
72
74
94
83
118
Name: _______________________________ Date: _______________
page 31
Fractions Challenge – Level C
Notes and Rough Work
Name: _______________________________ Date: _______________
page 32
Fractions Challenge – Level C
Notes and Rough Work (continued)
